Web - Amazon

We provide Linux to the World


We support WINRAR [What is this] - [Download .exe file(s) for Windows]

CLASSICISTRANIERI HOME PAGE - YOUTUBE CHANNEL
SITEMAP
Audiobooks by Valerio Di Stefano: Single Download - Complete Download [TAR] [WIM] [ZIP] [RAR] - Alphabetical Download  [TAR] [WIM] [ZIP] [RAR] - Download Instructions

Make a donation: IBAN: IT36M0708677020000000008016 - BIC/SWIFT:  ICRAITRRU60 - VALERIO DI STEFANO or
Privacy Policy Cookie Policy Terms and Conditions
Dyadic product - Wikipedia, the free encyclopedia

Dyadic product

From Wikipedia, the free encyclopedia

In mathematics, in particular multilinear algebra, the dyadic product

\mathbb{P} = \mathbf{u}\otimes\mathbf{v}

of a column vector \mathbf{u} and a row vector \mathbf{v} is the tensor product of the vectors. The result is a tensor of rank two (a matrix). It is a special case of the tensor product or Kronecker product, for vectors of the same dimension.

[edit] Example

\mathbf{u} \otimes \mathbf{v}  =  \begin{bmatrix}  u_1 \\  u_2 \\  u_3 \end{bmatrix}  \otimes  \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix}  =  \begin{bmatrix}  u_1v_1 & u_1v_2 & u_1v_3 \\  u_2v_1 & u_2v_2 & u_2v_3 \\  u_3v_1 & u_3v_2 & u_3v_3  \end{bmatrix}.

[edit] Definition

Using Einstein's summation convention, the dyadic product

\mathbf{u} \otimes \mathbf{v}

may be defined by

\mathbb{P}_{ij} = u_i v_j.

Writing out the sums, this becomes

\sum_{i,j}u_i v_j \mathbf{e}_i \otimes \mathbf{e}_j^T.

[edit] See also

Our "Network":

Project Gutenberg
https://gutenberg.classicistranieri.com

Encyclopaedia Britannica 1911
https://encyclopaediabritannica.classicistranieri.com

Librivox Audiobooks
https://librivox.classicistranieri.com

Linux Distributions
https://old.classicistranieri.com

Magnatune (MP3 Music)
https://magnatune.classicistranieri.com

Static Wikipedia (June 2008)
https://wikipedia.classicistranieri.com

Static Wikipedia (March 2008)
https://wikipedia2007.classicistranieri.com/mar2008/

Static Wikipedia (2007)
https://wikipedia2007.classicistranieri.com

Static Wikipedia (2006)
https://wikipedia2006.classicistranieri.com

Liber Liber
https://liberliber.classicistranieri.com

ZIM Files for Kiwix
https://zim.classicistranieri.com


Other Websites:

Bach - Goldberg Variations
https://www.goldbergvariations.org

Lazarillo de Tormes
https://www.lazarillodetormes.org

Madame Bovary
https://www.madamebovary.org

Il Fu Mattia Pascal
https://www.mattiapascal.it

The Voice in the Desert
https://www.thevoiceinthedesert.org

Confessione d'un amore fascista
https://www.amorefascista.it

Malinverno
https://www.malinverno.org

Debito formativo
https://www.debitoformativo.it

Adina Spire
https://www.adinaspire.com